Probits quarterly all banks
Emi
5/05/2021
Sample description
Fitting probit model.
Load data
db <- haven::read_dta('C:/Users/emi.ABLE-22868/OneDrive/UWA PhD/bankFailure/data/failures-1997-2001-quarterly.dta') %>%
dplyr::mutate(.,
FECHAdata = quarter(ymd("1960-01-01")+months(FECHA_Q*3), with_year=TRUE),
FECHAdataAnio = year(ymd("1960-01-01")+months(FECHA_Q*3)),
EXIT_DATE_Q = quarter(as_date(EXIT_DATE, origin=ymd('1960-01-01')), with_year=TRUE),
EXIT_DATE_Y = year(as_date(EXIT_DATE, origin=ymd('1960-01-01'))),
START_Q = quarter(as_date(FIRST_DATE, origin=ymd('1960-01-01')), with_year=TRUE),
.after = IDENT)Define sample
samsSpecs <- list('s1997q4' = c(samStart=1997.4, samEnd=2004.4, stateOwn=TRUE),
's1998q1' = c(samStart=1998.1, samEnd=2004.4, stateOwn=TRUE),
's1998q2' = c(samStart=1998.2, samEnd=2004.4, stateOwn=TRUE),
's1998q3' = c(samStart=1998.3, samEnd=2004.4, stateOwn=TRUE),
's1998q4' = c(samStart=1998.4, samEnd=2004.4, stateOwn=TRUE),
's1999q1' = c(samStart=1999.1, samEnd=2004.4, stateOwn=TRUE),
's1999q2' = c(samStart=1999.2, samEnd=2004.4, stateOwn=TRUE),
's1999q3' = c(samStart=1999.3, samEnd=2004.4, stateOwn=TRUE),
's1999q4' = c(samStart=1999.4, samEnd=2004.4, stateOwn=TRUE))The benchmark case I select all banks alive in 1997 and use their covariate to predict failure until time 2004.4 .
Here, I include banks alive on each t (instead of only banks alive on 1997q4).
Are state-owned banks included? 1
samStart contains the date at which the X covariates are considered (predictors), where samEnd is the last time failures are considered.
Estimation
State-owned banks are 4 (national) & 5 (provincial or municipal). Branches of foreign banks is 6, 5 is ‘cajas de credito’, 6 cia fcieras extranjero, 7 cia fcieras nacional.
r1 <- map(samsSpecs, function(samSpec) {
# samSpec <- samsSpecs[[1]]
sam <- db %>%
# Select observations of banks alive in 1997.4
#filter(START_Q <= 1997.4 & EXIT_DATE_Q > 1997.4) %>%
# Only complete observations
filter_all(all_vars(!is.na(.))) %>%
# Only observations at this time
filter(FECHAdata == samSpec['samStart'])
# ONly private banks
#filter(GRUPO_ID_UNI != 4 & GRUPO_ID_UNI !=5)
# Alternative you may want to incorporate banks that were created after 1997.4. Then,
# you consider all banks alive at samSpec['samStart'] quarter:
# sam <- db %>%
# # Select observations of banks alive at samSpec['samStart']
# filter(START_Q <= samSpec['samStart'] & EXIT_DATE_Q > samSpec['samStart']) %>%
# # Only complete observations
# filter_all(all_vars(!is.na(.))) %>%
# # Only observations at these time
# filter(FECHAdata == samSpec['samStart'])
#
# Bank covariates (X)
varsList <- c('ActivoN', 'C8Est_w', 'CAR_IRR_3A6', 'P_ROA', 'P_DEP_ARS_RATE', 'P_LOANS_ARS_RATE_W', 'APRSpNF_RATE_W', 'APR_USD_RATE', 'APR_RATE_W')
X <- sam %>% select(all_of(varsList))
# 1: survival, 0: failure during the sample period
Y <- if_else(sam$EXIT_DATE_Y <= samSpec['samEnd'], 0, 1)
# Table
desc <- tibble('N' = length(unique(sam$IDENT)),
'T' = length(unique(sam$FECHAdata)),
'NxT' = N*T,
'Avg n per panel' = sam %>%
select(FECHAdata, IDENT) %>%
group_by(IDENT) %>% summarise(n = n()) %$% mean(.$n),
'Avg IDENT' = mean(sam$IDENT),
'SampleStart' = min(sam$FECHAdata),
'SampleEnd' = max(sam$FECHAdata),
'Failure until' = samSpec['samEnd'],
'SurvivalRate' = round(mean(Y), digits=2))
descVars <- X %>%
summarise(across(all_of(varsList), list(
'min' = ~min(.x, na.rm=TRUE),
'median' = ~round(median(.x, na.rm=TRUE)),
'mean' = ~mean(.x, na.rm=TRUE),
'max' = ~round(max(.x, na.rm=TRUE)),
'SD' = ~round(sd(.x, na.rm=TRUE)) )))
# corr$r contains the correlation coefficients and corr$p the p-values (H0: r==0)
corr <- Hmisc::rcorr(as.matrix(X), type='pearson')
#map_dfr(samSpec['samStart']s, function(samSpec['samStart']) {
#
#
#})
#h <- rms::orm(Y ~ Xt$ActivoN + Xt$C8Est_w + Xt$CAR_IRR_3A6 + Xt$P_ROA + Xt$P_DEP_ARS_RATE + Xt$P_LOANS_ARS_RATE_W + Xt$APRSpNF_RATE_W + Xt$APR_USD_RATE + Xt$APR_RATE_W, family=probit)
p <- glm(as.matrix(Y) ~
X$ActivoN + X$C8Est_w + X$CAR_IRR_3A6 + X$P_ROA + X$P_DEP_ARS_RATE + X$P_LOANS_ARS_RATE_W + X$APRSpNF_RATE_W + X$APR_USD_RATE + X$APR_RATE_W,
family=binomial(link='logit'), x=TRUE)
list('desc' = desc, 'descVars' = descVars, 'corr'=corr, 'p' = p)
})## `summarise()` ungrouping output (override with `.groups` argument)
## `summarise()` ungrouping output (override with `.groups` argument)
## `summarise()` ungrouping output (override with `.groups` argument)
## `summarise()` ungrouping output (override with `.groups` argument)
## `summarise()` ungrouping output (override with `.groups` argument)
## `summarise()` ungrouping output (override with `.groups` argument)
## `summarise()` ungrouping output (override with `.groups` argument)
## `summarise()` ungrouping output (override with `.groups` argument)
## `summarise()` ungrouping output (override with `.groups` argument)Compute marginal effects
A \(1- \alpha\) confidence interval for \(\hat{\beta_k}\) is \(\hat{\beta_k} \pm z_{\frac{\alpha}{2}} \: \frac{\hat{\sigma_k}}{\sqrt{n}}\)
# OUtput is r2$s1997q4 containing a tibble with marginal effects for each variable
# Compute marginal effects
# Marginal probabilities
r2 <- map(r1, function(r) {
# r = r1$s97q4.Priv.01q4
pSummary <- summary.glm(r$p)
pMarginals <- dnorm( r$p$x %*% r$p$coefficients )
# Marginal effect of the average bank
x_Bar <- apply(r$p$x, MARGIN=2, mean) # Kx1 vector
pMarginalAvgBank <- dnorm( t(x_Bar) %*% r$p$coefficients)
pmap_dfr(as_tibble( pSummary$coefficients, rownames='var'), function(var, Estimate, `Std. Error`, ...) {
# CAMERON TRIVEDIR p467. Avergae Marginal effect of variable j is the average (over observations) of pdf(X Beta) * \hat{\beta}_j
tibble('samStart' = r$desc$SampleStart,
'samEnd' = r$desc$SampleStart,
'n' = NROW(r$p$y),
'var' = var,
'avgEffectMean' = mean(pMarginals * Estimate),
'avgEffectMin90' = avgEffectMean - 1.645 * (`Std. Error`)*(1/sqrt( n )),
'avgEffectMax90' = avgEffectMean + 1.645 * (`Std. Error`)*(1/sqrt( n )),
'effectAvgBankMean' = pMarginalAvgBank * Estimate,
'effectAvgBankMin90' = effectAvgBankMean - 1.645* (`Std. Error`)*(1/sqrt( n )),
'effectAvgBankMax90' = effectAvgBankMean + 1.645*(`Std. Error`)*(1/sqrt( n )))
})
}) Results
Descriptive statistics
t <- map2_dfr(r1, names(r1), function(r, samName) {
r$desc }) %>% t(.) %>%
as_tibble(., rownames='row_names')## Warning: The `x` argument of `as_tibble.matrix()` must have unique column names if `.name_repair` is omitted as of tibble 2.0.0.
## Using compatibility `.name_repair`.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.colnames(t) <- c('Feature', names(samsSpecs) )
t %>% DT::datatable(., rownames=FALSE) %>%
formatRound(columns=c(2:NCOL(t)))Means
tMeans <- map_dfr(r1, function(r) {
r$descVars %>% select(ends_with('_mean')) }) %>%
t(.) %>%
as_tibble(., rownames='row_names')
colnames(tMeans) <- c('Variable', names(samsSpecs) )
tMeans %>%
DT::datatable(., rownames=FALSE) %>% formatRound(columns=c(2:NCOL(tMeans)))Std Dev
tSDs <- map_dfr(r1, function(r) {
r$descVars %>% select(ends_with('_SD')) }) %>%
t(.) %>%
as_tibble(., rownames='row_names')
colnames(tSDs) <- c('Variable', names(samsSpecs) )
tSDs %>%
DT::datatable(., rownames=FALSE) %>% formatRound(columns=c(2:NCOL(tSDs)))Correlation coefficients
walk(r1, function(r) {
colnames(r$corr$P) <- str_c( colnames(r$corr$r), '_P')
corrData <- cbind(r$corr$r, r$corr$P) %>%
as_tibble(., rownames='Variable')
corrTable <- DT::datatable(corrData, rownames = FALSE,
caption='Correlation table. Bold correlations with p-value < 0.15',
extensions = 'FixedColumns',
options = list(dom = 'Variable', scrollX = TRUE, fixedColumns = TRUE))
# Add format for significant correlations (p-value < 0.15)
walk(colnames(r$corr$r), function(colName) {
#browser()
corrTable <<- formatStyle(corrTable,
colName, str_c(colName, '_P'),
fontWeight = styleInterval(c(0.15), c('bold', 'normal')))
corrTable <<- formatStyle(corrTable,
str_c(colName, '_P'),
visibility= 'hidden')
})
#browser()
print(corrTable %>% formatRound(columns=c(2:NCOL(corrData))))
#print('2')
})Average marginal effects
# Extract data on marginal effects for each sample
mEffects <- map_dfr(r2, function(sam) {
sam
})
plot_avg_m_effect <- function(varStr) {
dPlot <- filter(mEffects, var== !!str_c('X$',varStr)) %>%
mutate(
'avgEffectMin90' = avgEffectMin90*100,
'avgEffectMean' = avgEffectMean*100,
'avgEffectMax90' = avgEffectMax90*100,
'bar_length_radio' = (avgEffectMax90 - avgEffectMin90)/2,
'samStart_str' = str_c(samStart))
pInteractive <- plot_ly(data=dPlot,
x = ~samStart_str,
y = ~avgEffectMean,
type = 'scatter', mode = 'markers',
error_y = ~list(array = dPlot$bar_length_radio,
color = '#000000')) %>%
#name = ~Item,
#color = ~ Item,
#colors = c("dodgerblue3","deeppink3","lightgreen")),
layout(
title = 'Marginal effect of capital ratio on survival probability',
xaxis = list(type = 'category', title = 'Quarter of predictor'),
yaxis = list(title = 'Marginal effect x100'))
#range = c(0,7))
pStatic <- ggplot(data = dPlot,
mapping=aes(x=samStart, y=avgEffectMean)) +
geom_hline(yintercept=0) +
geom_pointrange(aes(ymin=avgEffectMin90, ymax=avgEffectMax90), colour='blue')
list('interactive' = pInteractive, 'static' = pStatic)
}Capital ratio (C8Est_w)
Plot marginal effect for capital ratio for different initial values of predictor variables.
plots <- plot_avg_m_effect('C8Est_w')
plots$interactive## Warning: `arrange_()` is deprecated as of dplyr 0.7.0.
## Please use `arrange()` instead.
## See vignette('programming') for more help
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.plots$static
Non-perfoaming loans
plots <- plot_avg_m_effect('CAR_IRR_3A6')
plots$interactiveplots$static
Deposits interest rate (P_DEP_ARS_RATE)
Plot marginal effect for Deposits interest rate for different initial values of predictor variables.
plots <- plot_avg_m_effect('P_DEP_ARS_RATE')
plots$interactiveplots$static
Loans interest rate (P_LOANS_ARS_RATE_W)
Plot marginal effect for Deposits interest rate for different initial values of predictor variables.
plots <- plot_avg_m_effect('P_LOANS_ARS_RATE_W')
plots$interactiveplots$static
PUblic sector exposure through loans (APRSpNF_RATE_W)
Plot marginal effect for PUblic sector exposure through loans for different initial values of predictor variables.
plots <- plot_avg_m_effect('APRSpNF_RATE_W')
plots$interactiveplots$static
USD loans (APR_USD_RATE)
Plot marginal effect for APR_USD_RATE for different initial values of predictor variables.
plots <- plot_avg_m_effect('APR_USD_RATE')
plots$interactiveplots$static
Loans to Assets ratio (APR_RATE_W)
Plot marginal effect for APR_RATE_W for different initial values of predictor variables.
plots <- plot_avg_m_effect('APR_RATE_W')
plots$interactiveplots$static
Marginal effects of average bank
Capital ratio (C8Est_w)
Plot marginal effect for capital ratio for different initial values of predictor variables.
plot_m_effect_avg_bank <- function(varStr) {
dPlot <- filter(mEffects, var == !!str_c('X$',varStr)) %>%
mutate(
'effectAvgBankMin90' = effectAvgBankMin90*100,
'effectAvgBankMean' = effectAvgBankMean*100,
'effectAvgBankMax90' = effectAvgBankMax90*100,
'bar_length_radio' = (effectAvgBankMax90 - effectAvgBankMin90)/2,
'samStart_str' = str_c(samStart))
pInteractive <- plot_ly(data=dPlot,
x = ~samStart_str,
y = ~effectAvgBankMean,
type = 'scatter', mode = 'markers',
error_y = ~list(array = dPlot$bar_length_radio,
color = '#000000')) %>%
#name = ~Item,
#color = ~ Item,
#colors = c("dodgerblue3","deeppink3","lightgreen")),
layout(
title = str_c('Marginal effect of ', varStr, ' on survival probability'),
xaxis = list(type = 'category', title = 'Quarter of predictor'),
yaxis = list(title = 'Marginal effect x100'))
#range = c(0,7))
pStatic <- ggplot(data = dPlot,
mapping=aes(x=samStart, y=effectAvgBankMean)) +
geom_hline(yintercept=0) +
geom_pointrange(aes(ymin=effectAvgBankMin90, ymax=effectAvgBankMax90), colour='blue')
list('interactive' = pInteractive, 'static' = pStatic)
}plots <- plot_m_effect_avg_bank('C8Est_w')
plots$interactiveplots$static
Non-perfoaming loans
plots <- plot_m_effect_avg_bank('CAR_IRR_3A6')
plots$interactiveplots$static
Deposits interest rate (P_DEP_ARS_RATE)
Plot marginal effect for Deposits interest rate for different initial values of predictor variables.
plots <- plot_m_effect_avg_bank('P_DEP_ARS_RATE')
plots$interactiveplots$static
Loans interest rate (P_LOANS_ARS_RATE_W)
Plot marginal effect for Deposits interest rate for different initial values of predictor variables.
plots <- plot_m_effect_avg_bank('P_LOANS_ARS_RATE_W')
plots$interactiveplots$static
PUblic sector exposure through loans (APRSpNF_RATE_W)
Plot marginal effect for PUblic sector exposure through loans for different initial values of predictor variables.
plots <- plot_m_effect_avg_bank('APRSpNF_RATE_W')
plots$interactiveplots$static
USD loans (APR_USD_RATE)
Plot marginal effect for APR_USD_RATE for different initial values of predictor variables.
plots <- plot_m_effect_avg_bank('APR_USD_RATE')
plots$interactiveplots$static
Loans to Assets ratio (APR_RATE_W)
Plot marginal effect for APR_RATE_W for different initial values of predictor variables.
plots <- plot_m_effect_avg_bank('APR_RATE_W')
plots$interactiveplots$static